Let's start with adding the database column first. Go to your phpMyAdmin, click on your prefix_adoptables database, and create a new column called "rarity", type varchar (40), collation latin1_swedish_ci, default can be set to Common (just in case you forget to update the species, at least they'll have a star).

With that finished, save these provided stars and names. Be sure to use the names I've provided! Upload them to your picuploads folder. Feel free to use your own custom images too if you'd rather have something else displayed instead of stars! Just keep the names.

Now you have some species rarity stars in place! Hopefully I've explained this well enough. The red star will only display if the adoptable is using its variant form. If it isn't using the variant form, the 10x10 transparent image will display, which appears as nothing to a user. Keep in mind, whenever you create a new adoptable species, you will need to manually edit its rarity field in your prefix_adoptables database, as by default, "Common" will always be used.

You can tinker with the code parts in order to include the stars on the myadopts.php and manage adopt pages.

You can also add more rarity options, and simply recolor the stars and upload them. This can be useful if you have quest, event, and/or holiday species. You could also even do away with rarities altogether and have element types, power types, etc! It's all up to you, go ahead and experiment!

Ooh, this is brilliant! My users have been asking about something like this! Thank you for sharing <3

I'm going to play around and see if I can incorporate this in the ACP :)
Edit:
That was actually way easier than I thought it'd be!

Only need to add some minor things;
.../admincp/adopt.php
Around line 52 you should see something starting with $mysidia->db->insert, the first of 3 that are right there. Add this into that string somewhere;

PHP Code:

"rarity" => $mysidia->input->post("rarity")

Now go to .../admincp/view/adoptview.php
Now find where you see a bunch of strings starting with $basicInfo and insert this chunk somewhere (I added mine right under the class section):

1.) If you'd like text only, then leave out the part where you add the <img src> code and instead just put {$this->adopt->getRarity()} and {$usealternates} (if you want variant text to display) or {$adopt->getRarity()} (I think this second one is for levelupview.php, someone wanna verify?)

2.) Yes, basically whatever you're calling your rarities in the database table is what you need to name your images. So if you have a rarity called "Fairy" then name your image "Fairy.png". Not sure if it's case sensitive but usually everything involving PHP is case sensitive. Though you can ignore this altogether if you aren't using images.

"wherever you have your adopts' stats displayed"? I don't know what this means..haha where would it be located in a basic Mys 1.3.4 file? c:

If you have public pet pages made, then pretty much wherever the adopt's stats (name, gender, personality, clicks, etc) are displayed, though really you could display it anywhere. If you don't have Kyttias's profile mod in place then this mod is kinda obsolete unless you're using it elsewhere (manage page for instance).